%0 Journal Article
%T A KIND OF F-INVERSE SPLIT MODULES
%J Journal of Algebraic Systems
%I Shahrood University of Technology
%Z 2345-5128
%A Hosseinpour, M.
%A Moniri Hamzekolaee, A. R.
%D 2020
%\ 01/01/2020
%V 7
%N 2
%P 167-178
%! A KIND OF F-INVERSE SPLIT MODULES
%K Rickart module
%K Z(M)-inverse split module
%K Z^2(M)-inverse split module
%R 10.22044/jas.2019.7211.1353
%X Let M be a right module over a ring R. In this manuscript, we shall study on a special case of F-inverse split modules where F is a fully invariant submodule of M introduced in [12]. We say M is Z 2(M)-inverse split provided f^(-1)(Z2(M)) is a direct summand of M for each endomorphism f of M. We prove that M is Z2(M)-inverse split if and only if M is a direct sum of Z2(M) and a Z2-torsionfree Rickart submodule. It is shown under some assumptions that the class of right perfect rings R for which every right R-module M is Z2(M)-inverse split (Z(M)-inverse split) is precisely that of right GV-rings.
%U http://jas.shahroodut.ac.ir/article_1587_488e6eda3752698fdd43a0b3c52a0dde.pdf